Material point method technical reference

This technical reference documentation outlines key background theory and numerical implementation details that underpin the material point method soil-structure interaction software.

Material point method basics

• Material Point Method overview

Large deformation formulation

• Kinematics
• Stress and strain measures
• Equilibrium equations for solid analysis
• Coupled equilibrium equations with rigid-body contact

Meshing

• Discretisation of the weak form on the background mesh
• Octree meshes
• Search algorithms

Basis functions

• Standard linear finite element basis functions
• Generalised interpolation basis functions
• Octree modifications

Material models

• Overview
• Isotropic linear elasticity
• Isotropic elasto-plasticity

Body forces

• Gravitational loads
• Discretisation on material points

Boundary conditions

• Neumann boundary conditions: free surfaces and tractions
• Dirichlet boundary conditions: displacement constraints

Small cut instability

• Ghost stabilisation

Rigid body representation and kinematics

• Faceted rigid body representation
• Rigid body kinematics
• Rigid body constraints

Coupled soil-structure interaction

• Contact detection
• Penalty contact formulation
• Coupled weak form equations

Linear solution

• Direct solvers (included within AMPSSIE)
• Iterative solvers (included within AMPSSIE)

Updating

• Material point updating
• Rigid body update
• Background mesh update/reset